Rigging questions - How do I make the drum of this revolver rotate only from the center of a barrel/barrel to frame question
As the barrel is symetric, you can find its center in edit mode by selecting all the vertices and use ShiftS (snap), then choose "Cursor to selected".



Now back to object mode. You can add a single bone armature and it will be created at the 3D cursor position (so it is centered to the barrel). Simply edit it (if you want as it is not mandatory here) in order to align the bone tail along the barrel (but keep the bone head in place along the same Y axis).

The barrel will rotate around the bone.


Edit (considering the comments) :

You can parent the bone placed above with the "barrel" (?) bone in blue below.
Go to pose mode for the "barrel" bone. Select the previous bone then select the "barrel" bone and CtrlP then choose "bone".



But as you can see, you may adjust the "barrel_joint" bone before doing all that :